Spot lamp rotation and dupliverts
1) Dupliverts + Origin offest

For your particular situation, where your base geometry is made by vertex and edges only you can obtain the effect by shifting the object's origin from the geometry.



Since you don't have faces but ony edges and vertex, vertex normals (which is the vector that the lamp will follow, blue in animated the image below) is always directed as the origin-to-vertex vector is, letting you achieve the desired result.





2) Duplifaces

As moving the origin may not be suitable for all the kind of workflows, you can duplifaces instead of dupliverts. You'll have more controle on the faces normals, which is the vector that your lamps will point to.



In the picture below you can see the target shape in orange, and in vivid yellow (active object) the shape parented with the lamp. It's the same shape, rotated by (360/6)/2=30° and scaled a bit to get the center of the face overlayed with the target shape vertices. Faces were created by extruding the edges.



Adjusting the Z difference between the innee and outer boundary edgeloop will give you full control of the lamps orientation.





3) Particle System

Emit particles by mesh's vertex, one for each (in your case the number must be 6) without any randomness (we must be sure to have one, and just one lamp for each vertex). Set Size=1 and Rotation checkbox enabled. Than rotate the Lamp on its Y axis by the choosen factor: